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So hopefully, you've had the time to kind of stare at what their bond is trying to

Â say and so on and so forth. Let's, we did the time line and formula. Just remember,

Â match the interest rate with the periodicity. Always make your interval of

Â thinking to compounding into it. And it will be pretty obvious when you're looking

Â at the bond or whatever the idea and so on, what it is. Match the compounding

Â integral interest rate. Let's do some calculations. And here, I'm going to go

Â over to my friend, the Excel. And there's some number from the past which we'll

Â ignore for the time. So, I'm going to stick in cell C. If you can see me,

Â hopefully you're fine. What I'm going to do is I'm going to do PV. Why? Because

Â I'm trying to do a PV here for bond, and what was the interest rate on similar

Â bond? Remember, it was six% but we are doing everything on my annual, 0.03. How

Â many number of periods? Twenty. What is the PMT? 30. And what is the future value?

Â You can do everything. What do you notice? I purposely picked this example first

Â construction. What do you notice? The price of the bond is equal to the face

Â value. Yes. Do you notice that? So, let's go here and I'll show you the intuition

Â for it. The price of the phase bond is the face value. That means today, you are the

Â phase exactly equal to the face value. Even though that face value is coming

Â twenty period from now. And the reason for it is, what is, what do you see the

Â relationship between coupon which is like a percentage and the interest rate? They

Â are both what? The same. 30 over a 1000 is 0.03. And what is my interest rate? 0.03.

Â So, what's happening? Very intuitively. The coupon is the numerator. It's coming

Â to you. But time is hurting you at the same rate so they cancel each other. And

Â what do you left with? $1,000. So, this is a neat thing that they'll say in the real

Â world that the bond is trading at face value, right? At Par. Par, P, A, R is face

Â value. Let's assume now that the interest rate in the real world is actually four%

Â per month, per year which is what per month? Two%. What does happen to the

Â price? It's gone up, it's created in face value. It's called trading at the premium.

Â Premium doesn't mean you're paying a higher price than you should. Premium

Â simply is relative , right. Discount is relative to . Okay, 1163. Quick question.

Â Why did this happened? Forget about the exact price and this is what I want you to

Â have in your gut-feeling for Finance not just numbers. You know the answer has to

Â be created in thousand and why is that? Notice the coupon is still 30, and it

Â cannot change once you've issued the bond because what's the coupon, who the term is

Â the coupon, the person is showing it and we are assuming the government is not

Â going to default in the thirtieth lays, right? But what can change is the market

Â rate that we using. So, the market rate is now two% and the coupon is three%. So,

Â what it's going to do? It's going to make the value of the bond go over a thousand,

Â simply because the value of getting it at the higher rate coupon than the discount rate.

Â Now, suppose the price is such that the rate of return that you are

Â getting in the similar instrument out there in the market is actually 8% and half of

Â eight is what, four%. What will happen to the price? It will go below a thousand ,

Â and it is called selling it to discount. Zero coupons always sell at a discount.

Â Zero coupon bonds always sell at the discount because there's no coupon

Â compensating for it whereas, coupon being bonds can and do sell it to discount but

Â what has to be true? Let's look at the parameters. The face value is a $1,000.

Â I'm not changing that. The coupon is 30, I'm not changing that. The n is twenty,

Â I'm not changing that, I'm standing to today, what did I changed? The interest

Â rate. Now, I'm hurting the bond's price at the higher rate than the coupon flowing in.

Â So, what happened because it's less than face value? So, this tells you something

Â about the pricing of bond which is this. Interest rates go up, price goes down.

Â But for a coupon paying bonds, government bonds, there's this neat relationship where, the interest rate and

Â the coupon rate are the same, the price of the bond has to be the face value. And

Â then, if the interest rate is higher, it's lower and the interest is

Â lower than the coupon rate, price is higher. So, let's try to take this

Â learning and graph it. So, you've done the calculations and I would really encourage

Â you to go back and do those calculations again, right? So, but I'll write out what you should find.

Â So, if coupon rate is greater than r, price will be greater than face value.

Â If coupon rate is less than r at a specific time, the price will be less

Â than the face value. If the coupon rate is equal to r, price will be equal to face

Â value. So, this is what you should find and just mess around with this because it

Â will help you. So, what I would like to show you know is a graph. And this graph

Â is important. Price, r, zero. It looks like this. So, the price of a bond falls

Â when interest rate goes up, alright? That's what it's showing and that makes

Â sense. So, if the interest rate is six% or three% per, what, six months. And the

Â coupon rate of this bond was what? Three%, what will the price be?A thousand. It just

Â did this, okay? One thing I really want to emphasize about this, coupon rate is not a

Â market thing, it's fixed by the government, don't ask me why, alright?

Â Because that's like getting into detail. Its something determined by their ability

Â to pay periodically versus face value, right? So, this curve is telling you the

Â relationship between bond prices and interest rate. And let me just give you

Â one little bottom line thing. Price goes down if r goes up. Second, short term

Â 8:23

versus long term. Which bonds are more price sensitive? In other words, if

Â interest rate changes, which bonds will be more sensitive, bonds that are, which

Â bond? Long term. Finally, whose price will jump around most? Zero coupon or coupon

Â bond? And let me, for simplicity, keep the maturities the same, whose price will bounce around more?

Â And that was kind of related to point number two. If you

Â have a zero coupon bond, where is all your money coming from. And supposing its

Â extending as maturity, all your money is coming ten years from now and you

Â attain the same face value coupon paying bond. What does happen with this

Â bond? Some of its money is coming earlier and not all is coming at the end. So, the

Â zero coupon bond will be more sensitive to changes in interest rate compared to and

Â otherwise identical coupon paying bond. It's not perfectly identical but the only

Â difference is the coupons. Okay. So, let's take this break because this is an

Â interesting point to think about and I want you to know this stuff inside out

Â because this is the simplest kinds of bonds and this is what the world talks

Â about all the time. Every government assures this and so on. So, we'll come

Â back to issues related to it. But in the next chunk, I will go and dig a little

Â deeper as we go further.

Â